Genera from an algebraic index theorem for supermanifolds
Quantum Algebra
2023-09-12 v3 Algebraic Topology
Differential Geometry
Abstract
We prove a super-version of Nest-Tsygan's algebraic index theorem. This work is inspired by the appearance of the same cobordism invariants in three related stories: index theory, trace methods in the deformation theory of algebras, and partition functions in quantum field theory. We show that one can recover the cobordism invariant appearing in supersymmetric quantum mechanics using trace methods for the associated deformation quantization problem.
Keywords
Cite
@article{arxiv.2204.05920,
title = {Genera from an algebraic index theorem for supermanifolds},
author = {Araminta Amabel},
journal= {arXiv preprint arXiv:2204.05920},
year = {2023}
}
Comments
52 pages. Corrections made to the computation in section 8.2